ΠΛΗ30 ΕΝΟΤΗΤΑ 3: ΚΑΝΟΝΙΚΕΣ ΓΛΩΣΣΕΣ Μάθηµα 3.2: Ντετερµινιστικά Πεπερασµένα Αυτόµατα ∆ηµήτρης Ψούνης
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30 3:
3.2:
-
.
.
1.
1.
2.
2 , 30, 3.2:
2.
1.
2.
3.
.
.
-
.
:
3 , 30, 3.2:
()
(-)
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B. 1. 1.
4 , 30, 3.2:
:
ML L
.
*x
Lx . ...
L
.
... LLx
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B. 1. 1.
5 , 30, 3.2:
1: L={w | w 00} :
A B 0 0
0,11
:
010010 101011
:
A B
1
x
x
-
B. 1. 1.
6 , 30, 3.2:
2: L={w | w 00} :
A B 0 0
1
01
11
3: L={w | w 00} :
A B 0 0
0,1
0,1
1 1
-
B. 1. 2.
7 , 30, 3.2:
:
( )
.
. .
:
, ,
( ) , ,
( )
-
B. 2. 1.
8 , 30, 3.2:
: ( ): () .
, 0 1.
:
( ) ( )
:
(...) .
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B. 2. 2. ()
9 , 30, 3.2:
:
(..) . (...)
.
:
.. / ...
, , .. .. ( , )
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B. 2. 3. ()
10 , 30, 3.2:
: 5-
M=(Q,,q0,,F): Q Q
(.. (q1,)=q2 q1 , q2)
Qq 0QQ :
QF
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B. 1. 3. ()
11 , 30, 3.2:
: L={w | w 00} :
A B 0 0
0,11
: M=(Q,,q0, , F) : Q={,,} ={0,1} q0=A :
F={}
A B
1
0 1
-
B. 2. 4. *
,
* :
12 , 30, 3.2:
: =(Q,,q0,,F). * :
*(q,)=q
*(q,w)=(*(q,w),) q: , w:
*: q w
w
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B. 1. 4. *
13 , 30, 3.2:
: L={w | w 00} :
A B 0 0
0,11
0 1
*(,100):
100 .
A B
1
=
==
==
==
)0,()0),0,((
)0),0),1,((()0),0),1),,(*(((
)0),0),1,(*(()0),10,(*(
)100,(*
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. 1. 1.
14 , 30, 3.2:
:
011}wwL |}*1,0{{ =
-
. 1. 2.
15 , 30, 3.2:
:
011}wwL |}*1,0{{ =
-
. 1. 3.
16 , 30, 3.2:
:
011}wwL |}*1,0{{ =
-
. 1. 4.
17 , 30, 3.2:
:
2}wwL |}*1,0{{ =
:
2}wwL |}*1,0{{ =
:
2}wwL |}*1,0{{ =
-
. 1. 5.
18 , 30, 3.2:
:
1}wwL |}*1,0{{ =
:
1}wwL |}*1,0{{ =
-
. 1. 6. ()
19 , 30, 3.2:
:
11}wwL |}*1,0{{ =
:
11}wwL |}*1,0{{ =
-
. 1. 7.
20 , 30, 3.2:
:
0 }wwL |}*1,0{{ =
-
. 1. 7.
21 , 30, 3.2:
:
0 1}wwL |}*1,0{{ =
-
. 1 ... :
L1={w{0,1}*| w 1100}
22 , 30, 3.2:
L2={w{0,1}*| w 0011}
L3={w{a,b}*| w 0101}
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. 2 .. :
L1=0*1*
23 , 30, 3.2:
L2=(1+01)*
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